Fischer random chess numbering scheme: Difference between revisions

Revision as of 07:45, 28 September 2019

Revision as of 05:32, 31 October 2019

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{{Refimprove|date=August 2012}}

The game [[Chess960Fischer Random Chess]], played with conventional [[chess]] [[chess piece|pieces]] and [[rules of chess|rules]], starts with a random selection of one of 960 positions for the pieces. Arrangements of the pieces are restricted so that the [[king (chess)|king]] is between the [[rook (chess)|rooks]] and the [[bishop (chess)|bishops]] are on different colored squares. In order to both select a valid arrangement and to then concisely discuss which randomly selected arrangement a particular game used, the '''Chess960Fischer Random Chess numbering scheme''' is used: a number between 0 and 959 indicates a valid arrangement and given an arrangement the number can be determined.

The Chess960Fischer Random Chess numbering scheme can be shown in the form of a simple two tables representation. Also a direct derivation of starting arrays exists for any given number from 0 to 959. This mapping of starting arrays and numbers stems from Reinhard Scharnagl and is now used worldwide for Chess960Fischer Random Chess. The enumeration has been published first in the internet and then 2004 in his (German language) book ''"Fischer-Random-Schach (FRC / Chess960) - Die revolutionäre Zukunft des Schachspiels (inkl. Computerschach)",'' {{ISBN|3-8334-1322-0}}.

== Two tables representation ==

These two tables will serve for a quick mapping of an arbitrary Chess960Fischer Random Chess starting position (short: SP) at White's base row to a random number between 0 and 959. First search for the same or the nearest smaller number from the King's Table. Then determine the difference (0 to 15) to the drawn number and select that matching bishops' positioning from the Bishop's Table. According to this first place both bishops at the first base row, then the six pieces in the sequence of the found row of the King's Table upon the six free places left over. Finally the black pieces will be placed symmetrically to White's base row.

=== Example ===

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== Direct derivation ==

White's [[Chess960Fischer Random Chess]] starting array can be derived from its number N (0 ... 959) as follows:

'''a)''' Divide N by 4, yielding quotient N2 and remainder B1. Place a '''Bishop''' upon the bright square corresponding to B1 (0=b, 1=d, 2=f, 3=h).

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'''e)''' There are three blank squares remaining; place a '''Rook''' in each of the outer two and the '''King''' in the middle one.

== Starting position IDs in Chess960Fischer Random Chess ==

For years, Reinhard Scharnagl has championed the desirability of giving each of the Chess960Fischer Random Chess starting positions (SP) a unique identification number (idn) in the range 0-959 or, perhaps, 1-960. He has presented his methods on the internet and in books. See the external references. As an application, a random number generator could make one probe into the range at hand for a random number, and produce a random SP. Late in 2005, the program Fritz9 became available. It has a Chess960Fischer Random Chess option, but, for some unexplained reason, it assigns idns to SPs in a different way. Rather than requiring a giant table with 960 entries, both methods can use some smaller tables and some arithmetic.

===Preliminaries===

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===Fritz9 methods===

Upon entry to Chess960Fischer Random Chess, Fritz9 prompts the user to enter a position idn or to "Draw Lots". If the user wishes to choose the first rank configuration of pieces, he/she must know how to get at the idn, but, unfortunately, Fritz9 does not use the standard method described above. The table below shows a quick way to get the Fritz9 idn for any SP.

For any SP, after ignoring the bishops, attention is given first to the knights (rather than to the queen). After taking account of the arrangement of the two knights in six squares (skipping over bishops), the queen is left with four possibilities: 0,1,2,3 (counting from the a-side of the board and skipping over bishops and knights). The queen's position is the number of hyphens to the left of the "Q" in the NQ-skeleton for the SP.

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==See also==

* [[Chess960Fischer Random Chess starting position]]

== External links ==

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*[http://www.mark-weeks.com/cfaa/chess960/c960strt.htm Chess960 start positions]

{{DEFAULTSORT:Chess960Fischer Random Chess Numbering Scheme}}

[[Category:Chess variants]]